Assesing Wine Qualities

Red Wine Exploration by Krushab Gandhi

---

In this project, we will explore a data set on wine quality. The dataset was obatined from the UCI Machine Learning Repository. The objective is to explore which chemical properties influence the quality of red wines.

We will start by exploring the data using the statistical program, R. As interesting relationships in the data are discovered, we will produce and refine plots to illustrate them.

---

Firstly, we will load the Wine dataset and analyze its structure

Wine <- read.csv('~/Desktop/Resume/Code-and-Dataset/wineQualityReds.csv')
str(Wine)

## 'data.frame':    1599 obs. of  13 variables:
##  $ X                   : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ fixed.acidity       : num  7.4 7.8 7.8 11.2 7.4 7.4 7.9 7.3 7.8 7.5 ...
##  $ volatile.acidity    : num  0.7 0.88 0.76 0.28 0.7 0.66 0.6 0.65 0.58 0.5 ...
##  $ citric.acid         : num  0 0 0.04 0.56 0 0 0.06 0 0.02 0.36 ...
##  $ residual.sugar      : num  1.9 2.6 2.3 1.9 1.9 1.8 1.6 1.2 2 6.1 ...
##  $ chlorides           : num  0.076 0.098 0.092 0.075 0.076 0.075 0.069 0.065 0.073 0.071 ...
##  $ free.sulfur.dioxide : num  11 25 15 17 11 13 15 15 9 17 ...
##  $ total.sulfur.dioxide: num  34 67 54 60 34 40 59 21 18 102 ...
##  $ density             : num  0.998 0.997 0.997 0.998 0.998 ...
##  $ pH                  : num  3.51 3.2 3.26 3.16 3.51 3.51 3.3 3.39 3.36 3.35 ...
##  $ sulphates           : num  0.56 0.68 0.65 0.58 0.56 0.56 0.46 0.47 0.57 0.8 ...
##  $ alcohol             : num  9.4 9.8 9.8 9.8 9.4 9.4 9.4 10 9.5 10.5 ...
##  $ quality             : int  5 5 5 6 5 5 5 7 7 5 ...

---

Let’s see the summary of the Wine dataset

summary(Wine)

##        X          fixed.acidity   volatile.acidity  citric.acid   
##  Min.   :   1.0   Min.   : 4.60   Min.   :0.1200   Min.   :0.000  
##  1st Qu.: 400.5   1st Qu.: 7.10   1st Qu.:0.3900   1st Qu.:0.090  
##  Median : 800.0   Median : 7.90   Median :0.5200   Median :0.260  
##  Mean   : 800.0   Mean   : 8.32   Mean   :0.5278   Mean   :0.271  
##  3rd Qu.:1199.5   3rd Qu.: 9.20   3rd Qu.:0.6400   3rd Qu.:0.420  
##  Max.   :1599.0   Max.   :15.90   Max.   :1.5800   Max.   :1.000  
##  residual.sugar     chlorides       free.sulfur.dioxide
##  Min.   : 0.900   Min.   :0.01200   Min.   : 1.00      
##  1st Qu.: 1.900   1st Qu.:0.07000   1st Qu.: 7.00      
##  Median : 2.200   Median :0.07900   Median :14.00      
##  Mean   : 2.539   Mean   :0.08747   Mean   :15.87      
##  3rd Qu.: 2.600   3rd Qu.:0.09000   3rd Qu.:21.00      
##  Max.   :15.500   Max.   :0.61100   Max.   :72.00      
##  total.sulfur.dioxide    density             pH          sulphates     
##  Min.   :  6.00       Min.   :0.9901   Min.   :2.740   Min.   :0.3300  
##  1st Qu.: 22.00       1st Qu.:0.9956   1st Qu.:3.210   1st Qu.:0.5500  
##  Median : 38.00       Median :0.9968   Median :3.310   Median :0.6200  
##  Mean   : 46.47       Mean   :0.9967   Mean   :3.311   Mean   :0.6581  
##  3rd Qu.: 62.00       3rd Qu.:0.9978   3rd Qu.:3.400   3rd Qu.:0.7300  
##  Max.   :289.00       Max.   :1.0037   Max.   :4.010   Max.   :2.0000  
##     alcohol         quality     
##  Min.   : 8.40   Min.   :3.000  
##  1st Qu.: 9.50   1st Qu.:5.000  
##  Median :10.20   Median :6.000  
##  Mean   :10.42   Mean   :5.636  
##  3rd Qu.:11.10   3rd Qu.:6.000  
##  Max.   :14.90   Max.   :8.000

---

• There are 1599 observations of 13 numeric variables.

• X appears to be the unique identifier.

• Quality is an ordered, categorical, discrete variable. From the literature, this was on a 0-10 scale, and was rated by at least 3 wine experts. The values ranged only from 3 to 8, with a mean of 5.64 and median of 6.

• All other variables seem to be continuous quantities with the exception of the .sulfur.dioxide suffixes

• From the variable descriptions, it appears that fixed.acidity ~ volatile.acidity and free.sulfur.dioxide ~ total.sulfur.dioxide may possibly be dependent subsets of each other.

---

Converting the X identifier into factors and quality attribute into numeric

Wine$quality <- as.numeric(Wine$quality)
Wine$X <- as.factor(Wine$X)

---

We use the table() function to calculate how many wines we have for each quality

table(Wine$quality)

## 
##   3   4   5   6   7   8 
##  10  53 681 638 199  18

---

UNIVARIATE PLOTS SECTION
Analyzing each and every attribute in the Wine dataset.

library(ggplot2)
library(gridExtra)
grid.arrange(qplot(Wine$fixed.acidity, geom = "histogram",  xlab = "Fixed Acidity", fill=I("blue"),
                   col=I("red")),
             qplot(Wine$volatile.acidity, geom = "histogram", xlab = "Volatile Acidity", fill=I("blue"),
                   col=I("red")),
             qplot(Wine$citric.acid, geom = "histogram", xlab = "Citric Acid", fill=I("blue"),
                   col=I("red")),
             qplot(Wine$residual.sugar, geom = "histogram", xlab = "Residual Sugar", fill=I("blue"),
                   col=I("red")),
             qplot(Wine$chlorides, geom = "histogram", binwidth = 0.03, xlab = "Chlorides", fill=I("blue"), 
                   col=I("red")),
             qplot(Wine$free.sulfur.dioxide, geom = "histogram", xlab = "Free Sulfur Dioxide", 
                   fill=I("blue"), col=I("red")),
             qplot(Wine$total.sulfur.dioxide, geom = "histogram", xlab = "Total Sulfur Dioxide",
                   fill=I("blue"), col=I("red")),
             qplot(Wine$density, geom = "histogram", xlab = "Density", fill=I("blue"),
                   col=I("red") ), 
             qplot(Wine$pH, geom = "histogram", xlab = "pH", fill=I("blue"),
                   col=I("red")),
             qplot(Wine$sulphates, geom = "histogram", xlab = "Sulphates", fill=I("blue"),
                   col=I("red")),
             qplot(Wine$alcohol, geom = "histogram", xlab = "Alcohol", fill=I("blue"), 
                   col=I("red")),
             qplot(Wine$quality, geom = "histogram", xlab = "Quality", fill=I("blue"), 
                   col=I("red")),
             ncol = 4, bottom = "Univariate Analysis - Histograms")

---

UNIVARIATE ANALYSIS
From the plots, we come to know the following:

• Looking at Wine Quality, we find that it forms a normal distribution, with most of the data structured around wine quality of 5 or 6.
• It appears that Density and pH are normally distributed, with a few outliers.
• Fixed and volatile acidity, sulfur dioxides, sulphates, and alcohol seem to be long-tailed.
• Qualitatively, residual sugar and chlorides have extreme outliers.
• Citric acid appeared to have a large number of zero values. This might be a case of non reporting.

---

Wine$rating <- ifelse(Wine$quality < 5, 'bad', ifelse(Wine$quality < 7, 'average', 'good'))
Wine$rating <- ordered(Wine$rating, levels = c('bad', 'average', 'good'))
summary(Wine$rating)

##     bad average    good 
##      63    1319     217

table(Wine$rating)

## 
##     bad average    good 
##      63    1319     217

---

To explore better, we created a new variable Rating, which classifies Wines into Good, Bad, and Average depending on their quality scores.
- BAD is Quality less than 5.
- AVERAGE is Quality less than 7 but greater than or equal to 5.
- GOOD is any number above and including 7.

---

ggplot(Wine,aes(x=fixed.acidity)) + geom_histogram(fill='red') + scale_x_log10(breaks=1:15) + 
       xlab('Fixed Acidity') + ylab('Count') + ggtitle('Histogram of Fixed Acidity Values') + 
       theme(plot.title = element_text(hjust=0.5))

ggplot(Wine) + geom_histogram(aes(x=volatile.acidity),fill='blue') + scale_x_log10(breaks=seq(0.1,1,0.1)) + 
  ggtitle("Histogram for volatile acidity") + theme(plot.title = element_text(hjust=0.5))

ggplot(Wine) + geom_histogram(aes(x=citric.acid), fill='green') + scale_x_log10() + 
  ggtitle("Histogram for citric acid") + theme(plot.title = element_text(hjust=0.5))

---

• As we could clearly see, citric acid was one feature that was found to be not normally distributed on a logarithmic scale. The transformation caused 132 data points to be in the infinite range, telling us that 132 values are 0, since we know Log(0) is infinity.

• While exploring the univariate histogram distributions, there did not appear to be any bimodal or multimodal distributions that would warrant sub-classification into categorical variables. I considered potentially splitting residual.sugar into ‘sweet wine’ and ‘dry wine’, but a residual sugar of greater than 45 g/L or g/m^3 is needed to classify as a sweet wine.

• We instantiated an ordered factor rating, classifying each wine sample as ‘bad’, ‘average’, or ‘good’.

---

library(plotly)
Wine$TAC.acidity <- Wine$fixed.acidity + Wine$volatile.acidity + Wine$citric.acid
qplot(Wine$TAC.acidity,main = 'Histogram of TAC Acidity (Tartaric+Acetic+Citric)')

# p <- plot_ly(Wine,x=~TAC.acidity) %>% layout(xaxis = list(title = "Histogram of TAC Acidity using plolty"))
# p ---- Using plotly to make the visualization more interactive

---

• Upon further examination of the data set documentation, it appears that fixed.acidity and volatile.acidity are different types of acids; tartaric acid and acetic acid. We decided to create a combined variable, TAC.acidity, containing the sum of tartaric, acetic, and citric acid.
• I have also used the plotly library to make the plot more interactive.

---

get_simple_boxplot <- function(column, ylab) {
return(qplot(data = Wine, x = '',
y = column, geom = 'boxplot',
xlab = '',
ylab = ylab))
}

grid.arrange(get_simple_boxplot(Wine$fixed.acidity, 'fixed acidity'),
get_simple_boxplot(Wine$volatile.acidity, 'volatile acidity'),
get_simple_boxplot(Wine$citric.acid, 'citric acid'),
get_simple_boxplot(Wine$TAC.acidity, 'TAC acidity'),
get_simple_boxplot(Wine$residual.sugar, 'residual sugar'),
get_simple_boxplot(Wine$chlorides, 'chlorides'),
get_simple_boxplot(Wine$free.sulfur.dioxide, 'free sulf. dioxide'),
get_simple_boxplot(Wine$total.sulfur.dioxide, 'total sulf. dioxide'),
get_simple_boxplot(Wine$density, 'density'),
get_simple_boxplot(Wine$pH, 'pH'),
get_simple_boxplot(Wine$sulphates, 'sulphates'),
get_simple_boxplot(Wine$alcohol, 'alcohol'),
ncol = 4)

---

• In univariate analysis, we chose not to tidy or adjust any data, short of plotting a select few on logarithmic scales. Again making use of the plolty library for interactive plots.
  
• Bivariate boxplots, with X as rating or quality, will be more interesting in showing trends with wine quality.

---

# plot_ly(Wine,y=~alcohol,type='box') ------- Using plotly to make the visualization more interactive

---

BIVARIATE PLOTS SECTION

---

set.seed(1)
Wine_sample <- Wine[,-which(names(Wine) %in% c('X', 'rating'))][sample(1:length(Wine$quality), 40), ]

get_bivariate_boxplot <- function(x, y, ylab) {
return(qplot(data = Wine, x = x, y = y, geom = 'boxplot', ylab = ylab))
}

grid.arrange(get_bivariate_boxplot(Wine$quality, Wine$fixed.acidity,
'fixed acidity'),
get_bivariate_boxplot(Wine$quality, Wine$volatile.acidity,
'volatile acidity'),
get_bivariate_boxplot(Wine$quality, Wine$citric.acid,
'citric acid'),
get_bivariate_boxplot(Wine$quality, Wine$TAC.acidity,
'TAC acidity'),
get_bivariate_boxplot(Wine$quality, log10(Wine$residual.sugar),
'residual sugar'),
get_bivariate_boxplot(Wine$quality, log10(Wine$chlorides),
'chlorides'),
get_bivariate_boxplot(Wine$quality, Wine$free.sulfur.dioxide,
'free sulf. dioxide'),
get_bivariate_boxplot(Wine$quality, Wine$total.sulfur.dioxide,
'total sulf. dioxide'),
get_bivariate_boxplot(Wine$quality, Wine$density,
'density'),
get_bivariate_boxplot(Wine$quality, Wine$pH,
'pH'),
get_bivariate_boxplot(Wine$quality, log10(Wine$sulphates),
'sulphates'),
get_bivariate_boxplot(Wine$quality, Wine$alcohol,
'alcohol'),
ncol = 4, bottom = "Here 'x' is quality")

grid.arrange(get_bivariate_boxplot(Wine$rating, Wine$fixed.acidity,
'fixed acidity'),
get_bivariate_boxplot(Wine$rating, Wine$volatile.acidity,
'volatile acidity'),
get_bivariate_boxplot(Wine$rating, Wine$citric.acid,
'citric acid'),
get_bivariate_boxplot(Wine$rating, Wine$TAC.acidity,
'TAC acidity'),
get_bivariate_boxplot(Wine$rating, log10(Wine$residual.sugar),
'residual sugar'),
get_bivariate_boxplot(Wine$rating, log10(Wine$chlorides),
'chlorides'),
get_bivariate_boxplot(Wine$rating, Wine$free.sulfur.dioxide,
'free sulf. dioxide'),
get_bivariate_boxplot(Wine$rating, Wine$total.sulfur.dioxide,
'total sulf. dioxide'),
get_bivariate_boxplot(Wine$rating, Wine$density,
'density'),
get_bivariate_boxplot(Wine$rating, Wine$pH,
'pH'),
get_bivariate_boxplot(Wine$rating, log10(Wine$sulphates),
'sulphates'),
get_bivariate_boxplot(Wine$rating, Wine$alcohol,
'alcohol'),
ncol = 4, bottom = "Here 'x' is rating")

---

Example using Plotly

---

# plot_ly(Wine,x=~quality,y=~alcohol) -------- Using plotly to make the visualization more interactive

---

Results from Bivariate Analysis are as follows:

From exploring these plots, it seems that a ‘good’ wine generally has these trends: - Higher fixed acidity (tartaric acid) and citric acid
- Lower volatile acidity (acetic acid)
- Lower pH (i.e. more acidic)
- Higher sulphates
- Higher alcohol
- To a lesser extent, lower chlorides and lower density
- Residual sugar and sulfur dioxides did not seem to have a dramatic impact on the quality or rating of the wines.
- Interestingly, it appears that different types of acid affect wine quality different; as such, TAC.acidity saw an attenuated trend, as the presence of volatile (acetic) acid accompanied decreased quality.

---

simple_cor_test <- function(x, y) {
return(cor.test(x, as.numeric(y))$estimate)
}

correlations <- c(
simple_cor_test(Wine$fixed.acidity, Wine$quality),
simple_cor_test(Wine$volatile.acidity, Wine$quality),
simple_cor_test(Wine$citric.acid, Wine$quality),
simple_cor_test(Wine$TAC.acidity, Wine$quality),
simple_cor_test(log10(Wine$residual.sugar), Wine$quality),
simple_cor_test(log10(Wine$chlorides), Wine$quality),
simple_cor_test(Wine$free.sulfur.dioxide, Wine$quality),
simple_cor_test(Wine$total.sulfur.dioxide, Wine$quality),
simple_cor_test(Wine$density, Wine$quality),
simple_cor_test(Wine$pH, Wine$quality),
simple_cor_test(log10(Wine$sulphates), Wine$quality),
simple_cor_test(Wine$alcohol, Wine$quality))

correlations

##         cor         cor         cor         cor         cor         cor 
##  0.12405165 -0.39055778  0.22637251  0.10375373  0.02353331 -0.17613996 
##         cor         cor         cor         cor         cor         cor 
## -0.05065606 -0.18510029 -0.17491923 -0.05773139  0.30864193  0.47616632

names(correlations) <- c('fixed.acidity', 'volatile.acidity', 'citric.acid',
'TAC.acidity', 'log10.residual.sugar',
'log10.chlordies', 'free.sulfur.dioxide',
'total.sulfur.dioxide', 'density', 'pH',
'log10.sulphates', 'alcohol')
correlations

##        fixed.acidity     volatile.acidity          citric.acid 
##           0.12405165          -0.39055778           0.22637251 
##          TAC.acidity log10.residual.sugar      log10.chlordies 
##           0.10375373           0.02353331          -0.17613996 
##  free.sulfur.dioxide total.sulfur.dioxide              density 
##          -0.05065606          -0.18510029          -0.17491923 
##                   pH      log10.sulphates              alcohol 
##          -0.05773139           0.30864193           0.47616632

---

By utilizing cor.test, I calculated the correlation for each of these variables against quality.

As we see, the top 4 come to be: - Alcohol
- Sulphates (log10)
- Volatile acidity
- Citric acid

Let’s plot them against each other using RATING as a facet.

---

ggplot(data=Wine,aes(x=citric.acid,y=alcohol))+facet_wrap(~rating)+geom_jitter(alpha=0.2)

ggplot(data = Wine, aes(x = log10(sulphates), y = alcohol)) +
  facet_wrap(~rating) +
  geom_jitter(alpha=0.2) 

ggplot(data = Wine, aes(x = volatile.acidity, y = alcohol)) +
  facet_wrap(~rating) +
  geom_point(alpha=0.2)

ggplot(data = Wine, aes(x = citric.acid, y = alcohol)) +
  facet_wrap(~rating) +
  geom_point(alpha=0.2)

ggplot(data = Wine, aes(x = volatile.acidity, y = log10(sulphates))) +
  facet_wrap(~rating) +
  geom_jitter(alpha=0.2)

ggplot(data = Wine, aes(x = citric.acid, y = log10(sulphates))) +
  facet_wrap(~rating) +
  geom_point(alpha=0.2)

ggplot(data = Wine, aes(x = citric.acid, y = volatile.acidity)) +
  facet_wrap(~rating) +
  geom_point(alpha=0.2)

---

• The relative value of these scatterplots are suspect; if anything, it illustrates how heavily alcohol content affects rating.
  
• The weakest bivariate relationship appeared to be alcohol vs. citric acid.
  
• The plots were nearly uniformly-distributed.
  
• The strongest relationship appeared to be volatile acididty vs. citric acid, which had a negative correlation.

Lets examining the acidity variables:

---

ggplot(data = Wine, aes(x = fixed.acidity, y = citric.acid)) +
  geom_point(alpha=0.3)

  cor.test(Wine$fixed.acidity, Wine$citric.acid)

## 
##  Pearson's product-moment correlation
## 
## data:  Wine$fixed.acidity and Wine$citric.acid
## t = 36.234, df = 1597, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.6438839 0.6977493
## sample estimates:
##       cor 
## 0.6717034

# plot_ly(Wine,x=~fixed.acidity,y=~citric.acid) ------ Using plotly to make the visualization more interactive

ggplot(data = Wine, aes(x = volatile.acidity, y = citric.acid)) +
  geom_point(alpha=0.3)

cor.test(Wine$volatile.acidity, Wine$citric.acid)

## 
##  Pearson's product-moment correlation
## 
## data:  Wine$volatile.acidity and Wine$citric.acid
## t = -26.489, df = 1597, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.5856550 -0.5174902
## sample estimates:
##        cor 
## -0.5524957

ggplot(data = Wine, aes(x = log10(TAC.acidity), y = pH)) +
  geom_point(alpha=0.3)

cor.test(log10(Wine$TAC.acidity), Wine$pH)

## 
##  Pearson's product-moment correlation
## 
## data:  log10(Wine$TAC.acidity) and Wine$pH
## t = -39.663, df = 1597, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.7283140 -0.6788653
## sample estimates:
##        cor 
## -0.7044435

---

Upon examining, I observed strong correlations between the acidity variables.

• Most notably, base 10 logarithm TAC.acidity correlated very well with pH. This is certainly expected, as pH is essentially a measure of acidity.

An interesting question to pose, using basic chemistry knowledge, is to ask what other components other than the measured acids are affecting pH. We can quantify this difference by building a predictive linear model, to predict pH based on TAC.acidity and capture the % difference as a new variable.

---

# Linear model
m <- lm(I(pH) ~ I(log10(TAC.acidity)), data = Wine)
Wine$pH.predictions <- predict(m, Wine)
# predict(m,Wine) --- to see linear prediction values

# (observed - expected) / expected
Wine$pH.error <- (Wine$pH.predictions - Wine$pH)/Wine$pH
# Wine$pH.error ----- to see linear prediction errors

ggplot(data = Wine, aes(x = quality, y = pH.error)) +
  geom_boxplot(outlier.colour = 'red')

# We can also add something interesting to our model, to check its accuracy.
# The RMS Error.

rmse <- function(error)
{
  sqrt(mean(error^2))
}

rmse(m$residuals)

## [1] 0.1095431

#Now, we train a Support Vector Machine.

library(e1071)

SVM <- svm(I(pH) ~ I(log10(TAC.acidity)), data = Wine)
Wine$pH.Predict.SVM <- predict(SVM,Wine)
# predict(SVM,Wine)  --- to see the SVM prediction values

Wine$pH.error.SVM <- (Wine$pH.Predict.SVM - Wine$pH)/Wine$pH

ggplot(data = Wine, aes(x = quality, y = pH.error.SVM)) +
  geom_boxplot(outlier.colour = 'red')

rmse(SVM$residuals)

## [1] 0.106785

---

Linear Model and Support Vector Machine

We see that a SVM functions slightly better than a LM.
- The first RMS is of the LM, the second of the SVM.
- The median % error hovered at or near zero for most wine qualities.
- Notably, wines rated with a quality of 3 had large negative error.
- We can interpret this finding by saying that for many of the ‘bad’ wines, total acidity from tartaric, acetic, and citric acids were a worse predictor of pH. Simply put, it is likely that there were other components–possibly impurities–that changed and affected the pH.

As annotated previously, we hypothesized that free.sulfur.dioxide and total.sulfur.dioxide were dependent on each other.
Plotting this:

---

ggplot(data = Wine, aes(x = free.sulfur.dioxide, y = total.sulfur.dioxide)) +
  geom_point(alpha=0.2) +
  geom_smooth(se=F)

## `geom_smooth()` using method = 'gam'

cor.test(Wine$free.sulfur.dioxide, Wine$total.sulfur.dioxide)

## 
##  Pearson's product-moment correlation
## 
## data:  Wine$free.sulfur.dioxide and Wine$total.sulfur.dioxide
## t = 35.84, df = 1597, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.6395786 0.6939740
## sample estimates:
##       cor 
## 0.6676665

---

• It is clear that there is a very strong relationship between the two.
  
• Aside from TAC.acidity, this seemed to be the strongest bivariate relationship.
  
• Additionally, despite the telling name descriptions, the clear ‘floor’ on this graph hints that free.sulfur.dioxide is a subset of total.sulfur.dioxide.

---

MULTIVARIATE PLOTS SECTION

---

ggplot(data = Wine,
       aes(x = citric.acid, y = volatile.acidity,
           color = rating)) +
  geom_jitter(alpha=1)

ggplot(data = Wine,
       aes(x = alcohol, y = log10(sulphates),
           color = rating)) +
  geom_point(alpha=0.2) 

ggplot(data = Wine,
       aes(x = pH, y = alcohol, color = rating)) +
  geom_point(alpha=0.2) 

ggplot(data = Wine,
       aes(x = pH, y = alcohol, color = rating)) +
  geom_point()

---

From the plots we come to know the following:

• We primarily examined the 4 features which showed high correlation with quality.
  
• These scatterplots were a bit crowded, so we faceted by rating AND by quality in the final plot to illustrate clearly and a little more about the population differences between good wines, average wines, and bad wines.
  
• It’s clear that a higher citric acid and lower volatile (acetic) acid contributes towards better wines. Likewise, better wines tended to have higher sulphates and alcohol content. Surprisingly, pH had very little visual impact on wine quality, and was shadowed by the larger impact of alcohol.
  
• Interestingly, this shows that what makes a good wine depends on the type of acids that are present.

---

FINAL PLOTS AND SUMMARY

---

PLOT ONE: EFFECTS OF ACID ON WINE QUALITY

---

### Plot One: Effects of Acid on Wine Quality
ggplot(data = Wine, aes(x = quality, y = fixed.acidity,
fill = quality)) + 
ylab('Fixed Acidity (g/dm^3)') +
xlab('Quality') +
geom_violin()+guides(fill=F)

grid.arrange(ggplot(data = Wine, aes(x = quality, y = fixed.acidity,
fill = quality)) + 
ylab('Fixed Acidity (g/dm^3)') +
xlab('Quality') +
geom_violin()+guides(fill=F),
ggplot(data = Wine, aes(x = quality, y = volatile.acidity,
fill = quality)) +
ylab('Volatile Acidity (g/dm^3)') +
xlab('Quality') +
geom_violin()+guides(fill=F), 
ggplot(data = Wine, aes(x = quality, y = citric.acid,
fill = quality)) +
ylab('Citric Acid (g/dm^3)') +
xlab('Quality') +
geom_violin()+guides(fill=F), 
ggplot(data = Wine, aes(x = quality, y = pH,
fill = quality)) +
ylab('pH') +
xlab('Quality') +
geom_violin()+guides(fill=F),top='Effects of Acid on Wine Quality')

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SUMMARY ONE

• These subplots were created to demonstrate the effect of acidity and pH on wine quality. Generally, higher acidity (or lower pH) is seen in highly-rated wines.
  
• To caveat this, a presence of volatile (acetic) acid negatively affected wine quality. Citric acidity had a high correlation with wine quality, while fixed (tartaric) acid had a smaller impact.

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PLOT TWO: EFFECTS OF ALCOHOL ON WINE QUALITY

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### Plot Two: Effect of Alcohol on Wine Quality
ggplot(data = Wine, aes(x = quality, y = alcohol,
fill = rating)) +
geom_boxplot(outlier.color = 'red') +
ggtitle('Alcohol Levels in Different Wine Qualities') +
xlab('Quality') +
ylab('Alcohol (% volume)')

---

SUMMARY TWO

• These boxplots demonstrate the effect of alcohol content on wine quality.
  
• Generally, higher alcohol content correlated with higher wine quality.
  
• However, as the outliers and intervals show, alchol content alone did not produce a higher quality.

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PLOT THREE: What makes good wines, good, and bad wines, bad?

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ggplot(data = subset(Wine, rating != 'average'),
aes(x = volatile.acidity, y = alcohol,
color = rating)) +
geom_point(alpha=0.4) +
ggtitle('Alcohol vs. Volatile Acidity and Wine Quality') +
xlab('Volatile Acidity (g / dm^3)') +
ylab('Alcohol (% volume)') + geom_smooth(method = 'lm',se=F)

# plot_ly(Wine,x=~rating,y=~volatile.acidity,z=~alcohol,type='scatter3d') ----- Using plotly to make the visualization more interactive

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SUMMARY THREE

• This is perhaps the most telling graph. We subsetted the data to remove the ‘average’ wines, or any wine with a rating of 5 or 6. As the correlation tests show, wine quality was affected most strongly by alcohol and volatile acidity.
  
• While the boundaries are not as clear cut or modal, it’s apparent that high volatile acidity–with few exceptions–kept wine quality down.
  
• A combination of high alcohol content and low volatile acidity produced better wines.

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MAIN CONCLUSION

• Through this exploratory data analysis, we were able to identify the key factors that determine and drive wine quality, mainly: alcohol content, sulphates, and acidity.
  
• It is important to note, however, that wine quality is ultimately a subjective measure, albeit measured by wine experts. That said, the correlations for these variables are within reasonable bounds.
• The graphs adequately illustrate the factors that make good wines ‘good’ and bad wines ‘bad’.
• Further study with inferential statistics could be done to quantitatively confirm these assertions.

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• One of the challenges that we faced was the lack of a clear analysis about the quality of our wine. The ordered factor “Quality” was not very helpful and to overcome this, we created another variable “Rating”.

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• To make predictions of wine quality and any other if required, we trained two models. As we saw before, the linear model and the Support Vector Machine.
• The SVM performed marginally better and we decided to stick with it if we had to make any more predictions.

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